The narrator introduces us to a woman who was beautiful, once had a loving marriage, and in the end, had no "luck." She feels burdened by her children. Only she and the children know she feels this way. The family has servants and some money but there is always the feeling that there is not enough money. They live "in style" but barely keep up this social status. The impression is that too much money went into "style" and not enough for substance.
The atmosphere in the house is haunted by the idea that they need more money. When Paul asks why they don't have a car, his mother tells him it is because they are poor. Why are they poor? Because they have no luck. Paul learns that luck is what causes people to have money and success. Paul goes off on his own to figure out how to find some luck.
Paul rides his rocking horse in an attempt to imagine his way to luck. His Uncle Oscar discovers that he is able to ride and come up with future winners of horse races. Paul had been practicing this and giving winners to one of the servants, Bassett. With Paul's picks, he, Uncle Oscar, and Bassett keep betting and keep winning. They arrange to have some of the winnings sent to Paul's mother in the guise of a family inheritance. It is supposed to be given over a period of years, but his mother greedily takes the sum all at once.
The feeling of needing more money haunts the house even more. This can be largely attributed to Paul's mother. To support his mother's growing need for money, Paul rides his horse more and more feverishly in order to keep finding winners ("luck"). In the end, the strain is too much for him.